I’ve never had this problem – export from AE as animation – drop into your FCP prject and export as uncompressed 8bit – PAL, if you’re using.
Note – FCP can have issues laying off 8bit files to tape – if you have a RAID – drop the 8bit to the raid and have the sequence read the file from there. Sometimes FCP will drop frames if reading 8bit from local drives.
Good luck.
Josh